The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.??
We can use the Pythagorean theorem to solve for the length of the edge of the square base.
The Pythagorean theorem states that for a right triangle, the square of the length of the hypotenuse (the slant height in this case) is equal to the sum of the squares of the two other sides.
Let x be the length of each side of the square base. Using the Pythagorean theorem, we have:
x^2 + x^2 = 436.5^2
Simplifying, we get:
2x^2 = 436.5^2
Dividing both sides by 2, we have:
x^2 = (436.5^2)/2
Taking the square root of both sides, we get:
x = √((436.5^2)/2)
Calculating this value, we find:
x ≈ 308.5 ft
So, the length of the edge of the square base is approximately 308.5 feet.